Optics and Image formation

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1 Optics and Image formation Pascal Chartrand chercheur-agrégé Département de Biochimie The Light Microscope Four centuries of history Vibrant current development One of the most widely used research tools 1

2 Main issues of Microscopy In order to observe small objects, three preconditions have to be fulfilled - Magnification - Resolution -Contrast Only fulfillment of these three conditions allows translation of information as accurately as possible from object into an image which represents that object. Waves vs. Photons vs. Rays Quantum wave-particle duality of light Rays: photon trajectories Rays: propagation direction of waves Light as a wave 2

3 Light waves frequency = v = oscillations per seconds (Hz) Rays are perpendicular to wavefronts 3

4 The electromagnetic spectrum shorter, higher v longer, lower v Energy of photons E = hv where: h= Planck s constant (6,63x10-34 J.sec) v= frequency of photons Therefore, blue light is more energetic than red light 4

5 Light interacts with matter It can be: - absorbed - diffracted - reflected - refracted Refraction 5

6 Light velocity c= where: c= speed of light in a vacuum (3x10 8 m/sec) = wavelenght = frequency of photons However, the speed of light is not constant and vary depending on the medium Index of refraction: velocity of light in a material compared to the velocity of light in air v= c/n where v= velocity of light in a medium in the air or in a vacuum, n=1 Light travels more slowly in matter The speed ratio is the Index of Refraction, n v = c/n n = 1 n > 1 n = 1 6

7 Refractive Index Examples Vacuum 1 Air Water Cytoplasm ? Glycerol (anhydrous) Immersion oil Fused silica 1.46 Optical glasses Diamond Depends on wavelength and temperature How refraction works Refraction occurs when a wave front moves into an interface between two substances with different refractive indices Wave Front Air Air 90 o Not 90 o Glass Glass 7

8 Refraction by an Interface Refractive index n 1 = 1 Speed = c Incident wave 1 r Reflected wave Refractive index n 2 Speed = c/n /n 2 Refracted wave Snell s law: n 1 Sin( 1 ) = n 2 Sin( 2 ) Mirror law: r = 1 Which Direction? n 1 n 2 > n 1 Refraction goes towards the normal in the higher-index medium 8

9 Refraction and lenses Lenses Parallel light rays coming from infinity F= focal plane or focal point FL= focal length Axis: axis of the lens Refraction of light rays on the surface of the glass of a bi-convex lens leads to the convergence of the rays toward a point beyond the lens, called focal plane 9

10 Ray Tracing Rules of Thumb (for thin ideal lenses) Parallel rays converge at the focal plane Rays that cross in the focal plane end up parallel f f Rays through the lens center are unaffected What happen if you put an object in front of a lens? The three rules of refraction: 1) an incident ray traveling parallel to the axis of the lens will refract through the lens and travel through the focal point on the opposite side of the lens 2) an indicent ray travelling through the center of the lens will continue in the same direction that when it entered the lens 3) an incident ray travelling through the focal point on the way to the lens will refract through the lens and emerge parallel to the axis of the lens 10

11 What happen if you put an object in front of a lens? When a set of incident and refracted rays are drawn for several points upon a vertical object, each reflected ray intersect at locations which form a vertical image To simplify ray diagrams, only two sets of rays from a single point are usually showed Lenses and magnification An object located over 2X the distance of the focal point (2F) forms a small inverted image of an object on the opposite side of a lens An object located between F and 2F forms a large inverted image of an object on the opposite side of a lens The closer an object is to the focal point, the larger its image will be 11

12 Lenses and magnification object f f image d 1 d 2 p q The lens law: 1 p + 1 q = 1 f Magnification: d 2 M = = d 1 q p Lenses and magnification What happen if an object is at the focal point of a lens? At the focal point, all the refracted rays are parallel, and do not converge toward a specific point to form an image of the object - therefore, there is no image of the object 12

13 Lenses and magnification What happen if an object is between the focal point and the lens? All the refracted rays are divergent, and do not converge toward a specific point to form an image of the object - However, there is a virtual image of the object is formed. This virtual image is bigger than the image, upright and located in front of the lens The compound microscope specimen objective f f Intermediate image plane (I.I.P) I.I.P ocular f f f f f f specimen I.I.P objective ocular 13

14 Back focal plane Back focal plane f 0 Object f 0 f 0 objective Tube lens Rays that leave the object with the same angle meet in the objective s back focal plane The Compound Microscope Exit pupil Eyepiece Primary or intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane 14

15 The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane Microscope conjugate planes: Planes which are in focus with each other Field or Image forming conjugate set The Compound Microscope Eye Eyepiece Tube lens Final image Exit pupil Intermediate image plane Objective Sample Back focal plane (pupil) Object plane 15

16 The Compound Microscope Microscope conjugate planes: Planes which are in focus with each other Aperture or Illumination conjugate set Eye Eyepiece Tube lens Objective Sample Final image Exit pupil Intermediate image plane Back focal plane (pupil) Object plane Finite vs infinity-corrected microscope Finite-tube lenght microscope 160 mm specimen I.I.P objective ocular 16

17 Finite vs infinity-corrected microscope Infinity-corrected microscope Parallel light beam (infinity space) specimen I.I.P objective tube lens ocular Magnification of microscope = magnification of objective x magnification of the ocular Function of any microscopy is NOT simply to magnify! Function of the microscope is to RESOLVE fine detail. 17

18 Resolution RESOLUTION means objects can be seen as separate objects Resolution Resolution The resolution of a microscope is the shortest distance two points that can be separated and still be observed as 2 points Well resolved just resolved Not resolved d N.A. MORE IMPORTANT THAN MAGNIFICATION!! 18

19 WHAT DETERMINES RESOLUTION? 1. Contrast is necessary to detect detail (edges) from background 2. Diffraction fundamentally limits resolution diffraction occurs at the objective lens aperture Diffraction 19

20 The Huygens principle and diffraction Huygens Principle All points on a wave front act as point sources of spherically propagating wavelets. At a short time Δt later, the new wave front is the unique surface tangent to all the forward-propagating wavelets. In phase Interference constructive interference + = Opposite phase + = destructive interference 20

21 Diffraction of waves passing through a single slit negative interference positive interference Single-slit diffraction pattern 21

22 Diffraction by an aperture drawn as waves Light spreads to new angles Larger aperture weaker diffraction Diffraction by an aperture drawn as rays The pure, far-field diffraction pattern is formed at infinity Tube lens or can be formed at a finite distance by a lens Objective pupil Intermediate image as happens in a microscope 22

23

24 Aperture and Resolution Diffraction spot on image plane Objective Tube lens Intermediate image plane Sample Back focal plane aperture Aperture and Resolution Diffraction spot on image plane Objective Tube lens Intermediate image plane Sample Back focal plane aperture 1

25 Aperture and Resolution Diffraction spot on image plane Objective Tube lens Intermediate image plane Sample Back focal plane aperture Aperture and Resolution Diffraction spot on image plane Objective Tube lens Intermediate image plane Sample Back focal plane aperture Image resolution improves with aperture size Numerical Aperture (NA) NA = n sin( ) where: = light gathering angle n = refractive index of sample 2

26 Numerical Aperture of objectives 100X / 0.95 NA = X / 0.20 NA = 11.5 Role of immersion medium NA=n sin (α) Refractive indices: Air: Water: 1.33 Glycerol: 1.47 Oil: 1.52 Immersion media increases the NA of an objective or a condenser by bringing the beams with higher incidence angle into the light path 3

27 The Rayleigh criterion and resolution Generally accepted criterion of resolution Single point source Just resolved d Well resolved Central maximum of one peak overlies 1 st minimum of neighboring peak The Rayleigh criterion and resolution Minimal distance between two points of an object that can be resolved Rayleigh criterion: d = 0.61 for self-luminous object) N.A. N.A. : Numerical aperture of the objective Ex. : NA = 1.4, = 520 nm (GFP, FITC ) d = 226 nm (human eye: d ~ 100 μm) Thus, the best resolution that can be achieved by an optical microscope is ~ 200 nm 4

28 Effect of wavelength on resolution Decreasing wavelength increases the resolution between two points Objective of NA 0.95 d = nm d = nm The point spread function (PSF) The Airy disk correspond to a slice of a point spread function x x z y The PSF correspond to the image produced by the microscope of a point source of light 5

29 PSF and axial (Z) resolution The axial resolution can be defined as FWHM = the full width at half maximal intensity of a z line of a point source Z-POSITION FWHM INTENSITY or d = 2 n for = 520 nm, NA= 1,4, n= 1,52 NA 2 the axial resolution is ~ 820 nm Contrast Live cells are largely transparent, absorbing almost no light and scatter relatively little - little contrast between cell and surrounding medium How can we increase this contrast? brightfield darkfield phase contrast Differential interference contrast 6

30 Which properties of light can we change to increase contrast Amplitude => increase illumination intensity or put in an absorbent stain Wavelength => use fluorescent molecules Direction of propagation: Look only at light refracted by sample (dark field microscopy) Velocity=> Phase; Altering phase of incident light can lead to interference with background light (Phase contrast, DIC) Effect of the specimen on the phase of incident light - Amplitude specimen changes the intensity of incident light - Phase specimen changes the phase of incident light - Most unstained biological specimens are phase ones 7

31 A Diffracted Light Background Light 1/4 Phase Contrast Phase Contrast produces destructive interference. A) When incident light pass through a specimen, the diffracted light is ¼ wavelength out of phase with the background light. B Diffracted Light Background Light 1/2 Destructive interference B) A Phase plate, at the back focal plane of the objective, further retards diffracted light by ¼ wavelength - This creates a ½ wavelength difference between the background and diffracted light. Phase Contrast Brightfield Phase Contrast Benefits and Negatives of Phase Contrast Microscopy Benefits Much better resolution (dark edges) Good for unstained cells (Tissue Culture) Better Contrast Negatives White halo around the edges A Phase Ring Equipped Objective is required Optimized for 548nm wavelength 8

32 Differential interference Contrast (DIC) 4 3 1) A single ray of light is split by the Wollaston prism - generates 2 rays separated by a distance of ~ 0,2 um and slightly out of phase (90 ) 2) Both rays go through the specimen 1 2 3) A second Wollaston prism combines the split rays 4) An analyzer brings the rays in the same plane - if both rays are in phase, this results in positive interference Differential interference Contrast (DIC) A) If both rays go through a medium with the same refractive index, both ray will stay in phase, leading to positive interference when both rays combine (bright) B) If one of the two rays goes through the cytoplasm of a cell, this will result in a shift of its phase compared to the sister ray, leading to negative interference when both rays combine (dark-grey) C) If both rays go through a cell, both will have the same phase alteration, leading to positive interference when both rays combine (bright) 9

33 Differential Interference Contrast Phase Contrast DIC Benefits and Negatives of DIC Microscopy Benefits Best Resolution (3D effect) Best depth discrimination (but be careful - What you see is NOT always what you get) Good contrast Negatives Cannot do both low power and high power DIC (lower Wallaston) Due to use of polarizers, DIC cannot be used with plastic dishes. Change in RI can be mistaken for depth 10

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